This work has examined two finite element methods for solving the vector transport equation with the lowest-order Raviart-Thomas elements.
This was motivated by increasing the order of accuracy when compared with a standard upwind discretisation.
The first scheme is an extension to the transport schemes of [1]}, and solves the transport equation in advective form and recovers the field in a higher-order function space to transport it there.
The second scheme is a take on the mixed finite element formulation of [2]}, applied to the vector transport equation and using a residual based stabilisation concept of [3]}.
This is written in a vorticity form, solving a problem for both the transported vector and its vorticity.
As demonstrated through the test cases in Section , both schemes do have improved accuracy.
